The Zeeman splitting of the metastable 5
D3/2 level of
138Ba+ in a magnetic field of 6 T has been measured in a laser-microwave double resonance experiment in a Penning ion trap. The magnetic field at the ion's position is determined by the cyclotron frequency of electrons stored in the same trap. From the ratio of both transition frequencies we obtain a
gJ value of 0.799 327 8(3). As a by-product, we confirmed earlier measurements on the 6
S1/2 ground-state
gJ factor to 2.002 492 2(10). The precision in both experiments is sufficient to test relativistic many-body calculations. \textcopyright{} 1996 The American Physical Society.